`e)x²-3x-10=0`
`⇔x²-5x+2x-10=0`
`⇔x(x-5)+2(x-5)=0`
`⇔(x-5)(x+2)=0`
`⇔`\(\left[ \begin{array}{l}x-5=0\\x+2=0\end{array} \right.\)
`⇔`\(\left[ \begin{array}{l}x=5\\x=-2\end{array} \right.\)
Vậy `x=5` hoặc `x=-2`
`f)x²-8x+19=0`
`⇔x²-8x+16+3=0`
`⇔(x²-8x+16)+3=0`
`⇔(x-4)²+3=0`
Ta có:`(x-4)²≥0` với `∀x`
`⇒(x-4)²+3≥3>0` với `∀x`
`⇒` phương trình vô nghiệm
`g)x²-2x-10=0`
`⇔x²-2x+1-11=0`
`⇔(x²-2x+1)-11=0`
`⇔(x-1)²=11`
`⇔`\(\left[ \begin{array}{l}x-1=\sqrt[]{11}\\x-1=-\sqrt[]{11}\end{array} \right.\)
`⇔`\(\left[ \begin{array}{l}x=\sqrt[]{11}+1\\x=-\sqrt[]{11}+1\end{array} \right.\)
Vậy `x=`$\sqrt[]{11}+1$ hoặc `x=-`$\sqrt[]{11}+1$
`k)2x²-9x-5=0`
`⇔2x²-10x+x-5=0`
`⇔2x(x-5)+(x-5)=0`
`⇔(x-5)(2x+1)=0`
`⇔`\(\left[ \begin{array}{l}x-5=0\\2x+1=0\end{array} \right.\)
`⇔`\(\left[ \begin{array}{l}x=5\\x=-\dfrac{1}{2}\end{array} \right.\)
Vậy `x=5` hoặc `x=-1/2`